Nuprl Lemma : ss-open-or_wf
∀[X:SeparationSpace]. ∀[T:Type]. ∀[F:T ⟶ Open(X)]. (⋃x:T.F[x] ∈ Open(X))
Proof
Definitions occuring in Statement :
ss-open-or: ⋃x:T.F[x],
ss-open: Open(X),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-open-or: ⋃x:T.F[x],
ss-open: Open(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
exists_wf,
subtype_rel_self,
ss-basic_wf,
ss-open_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
functionEquality,
cumulativity,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[T:Type]. \mforall{}[F:T {}\mrightarrow{} Open(X)]. (\mcup{}x:T.F[x] \mmember{} Open(X))
Date html generated:
2020_05_20-PM-01_22_42
Last ObjectModification:
2018_07_06-PM-05_00_08
Theory : intuitionistic!topology
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